How to calculate cylinder height

How to calculate cylinder height

The cylinder has height which is perpendicular to two of its bases. The way of determination of its length depends on a set of basic data. In particular, diameter, the area, section diagonal can be those.

Instruction

1. For any figures there is such term as height. Height usually is called what measured size - or figures in vertical position. At a cylinder height is the line perpendicular to two of its parallel bases. Also it has forming. Forming a cylinder is a line which rotation the cylinder turns out. It, unlike forming other figures, for example a cone, coincides with height. Let's consider a formula by means of which it is possible to find height: V=πR^2*H where R is the radius of the basis of a cylinder, H is required height. If instead of radius diameter is given, this formula changes as follows: V=πR^2*H=1/4πD^2*HСоответственно, height of a cylinder is equal: H=V/πR^2=4V/D^2

2. Also height can be determined, proceeding from diameter and the area of a cylinder. There is an area side and the area of a full surface of a cylinder. The part of a surface of a cylinder limited to a cylindrical surface call a side surface of a cylinder. The area of a full surface of a cylinder includes also the area of its bases. The area of a side surface of a cylinder is calculated on the following formula: S=2πRHПреобразовав this expression, find height: H=S/2πRЕсли is given the area of a full surface of a cylinder, calculate height in a bit different way. The area of a full surface of a cylinder is equal: S=2πR(H+R) transform this formula as shown below In the beginning: Find S=2πRH+2πRЗатем height: H=S-2πR/2πR

3. Through a cylinder it is possible to carry out rectangular section. Width of this section will coincide with diameters of the bases, and length - with forming figures which are equal to height. If to carry out diagonal through this section, then it is possible to notice easily that the rectangular triangle is formed. In this case diagonal is a triangle hypotenuse, a leg - diameter, and the second leg - height and forming a cylinder. Then height can be found on Pythagorean theorem: b^2 =sqrt (c^2-a^2)

Author: «MirrorInfo» Dream Team


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